Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC) run explor
es the space of phylogenetic trees. In this paper, we investigate the Monte Carlo error of phylogenies, focusing on high-dimensional summaries of the posterior distribution, including variability in estimated edge/branch (known in phylogenetics as split) probabilities and tree probabilities, and variability in the estimated summary tree. Specifically, we ask if there is any measure of effective sample size (ESS) applicable to phylogenetic trees which is capable of capturing the Monte Carlo error of these three summary measures. We find that there are some ESS measures capable of capturing the error inherent in using MCMC samples to approximate the posterior distributions on phylogenies. We term these tree ESS measures, and identify a set of three which are useful in practice for assessing the Monte Carlo error. Lastly, we present visualization tools that can improve comparisons between multiple independent MCMC runs by accounting for the Monte Carlo error present in each chain. Our results indicate that common post-MCMC workflows are insufficient to capture the inherent Monte Carlo error of the tree, and highlight the need for both within-chain mixing and between-chain convergence assessments.
We consider a population constituted by two types of individuals; each of them can produce offspring in two different islands (as a particular case the islands can be interpreted as active or dormant individuals). We model the evolution of the popula
tion of each type using a two-type Feller diffusion with immigration, and we study the frequency of one of the types, in each island, when the total population size in each island is forced to be constant at a dense set of times. This leads to the solution of a SDE which we call the asymmetric two-island frequency process. We derive properties of this process and obtain a large population limit when the total size of each island tends to infinity. Additionally, we compute the fluctuations of the process around its deterministic limit. We establish conditions under which the asymmetric two-island frequency process has a moment dual. The dual is a continuous-time two-dimensional Markov chain that can be interpreted in terms of mutation, branching, pairwise branching, coalescence, and a novel mixed selection-migration term. Also, we conduct a stability analysis of the limiting deterministic dynamical system and present some numerical results to study fixation and a new form of balancing selection. When restricting to the seedbank model, we observe that some combinations of the parameters lead to balancing selection. Besides finding yet another way in which genetic reservoirs increase the genetic variability, we find that if a population that sustains a seedbank competes with one that does not, the seed producers will have a selective advantage if they reproduce faster, but will not have a selective disadvantage if they reproduce slower: their worst case scenario is balancing selection.
Arid zones contain a diverse set of microbes capable of survival under dry conditions, some of which can form relationships with plants under drought stress conditions to improve plant health. We studied squash (Cucurbita pepo L.) root microbiome und
er historically arid and humid sites, both in situ and performing a common garden experiment. Plants were grown in soils from sites with different drought levels, using in situ collected soils as the microbial source. We described and analyzed bacterial diversity by 16S rRNA gene sequencing (N=48) from the soil, rhizosphere, and endosphere. Proteobacteria were the most abundant phylum present in humid and arid samples, while Actinobacteriota abundance was higher in arid ones. The Beta-diversity analyses showed split microbiomes between arid and humid microbiomes, and aridity and soil pH levels could explain it. These differences between humid and arid microbiomes were maintained in the common garden experiment, showing that it is possible to transplant in situ diversity to the greenhouse. We detected a total of 1009 bacterial genera; 199 exclusively associated with roots under arid conditions. With shotgun metagenomic sequencing of rhizospheres (N=6), we identified 2969 protein families in the squash core metagenome and found an increased number of exclusively protein families from arid (924) than humid samples (158). We found arid conditions enriched genes involved in protein degradation and folding, oxidative stress, compatible solute synthesis, and ion pumps associated with osmotic regulation. Plant phenotyping allowed us to correlate bacterial communities with plant growth. Our study revealed that it is possible to evaluate microbiome diversity ex-situ and identify critical species and genes involved in plant-microbe interactions in historically arid locations.
The COVID-19 pandemic, caused by the coronavirus SARS-CoV-2, has led to a wide range of non-pharmaceutical interventions being implemented around the world to curb transmission. However, the economic and social costs of some of these measures, especi
ally lockdowns, has been high. An alternative and widely discussed public health strategy for the COVID-19 pandemic would have been to shield those most vulnerable to COVID-19, while allowing infection to spread among lower risk individuals with the aim of reaching herd immunity. Here we retrospectively explore the effectiveness of this strategy, showing that even under the unrealistic assumption of perfect shielding, hospitals would have been rapidly overwhelmed with many avoidable deaths among lower risk individuals. Crucially, even a small (20%) reduction in the effectiveness of shielding would have likely led to a large increase (>150%) in the number of deaths compared to perfect shielding. Our findings demonstrate that shielding the vulnerable while allowing infections to spread among the wider population would not have been a viable public health strategy for COVID-19, and is unlikely to be effective for future pandemics.
We study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease. Such measures are currently
either implemented or at least discussed in numerous countries worldwide to ward off a potential new wave of COVID-19 across Europe. They come in the form of Health Passes (HP), which grant full access to public life only to individuals with a certificate that proves that they have either been fully vaccinated, have recovered from a previous infection or have recently tested negative to SARS-Cov-19 . We develop both a compartmental model as well as an epidemic Renormalisation Group approach, which is capable of describing the dynamics over a longer period of time, notably an entire epidemiological wave. Introducing differe
Since Press and Dysons ingenious discovery of ZD (zero-determinant) strategy in the repeated Prisoners Dilemma game, several studies have confirmed the existence of ZD strategy in repeated multiplayer social dilemmas. However, few researches study th
e evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a newly proposed state-clustering method to theoretically analyze the evolutionary dynamics of two representative ZD strategies: generous ZD strategies and extortionate ZD strategies. Apart from the competitions between the two strategies and some classical strategies, we consider two new settings for multiplayer ZD strategies: competitions in the whole ZD strategy space and competitions in the space of all memory-1 strategies. Besides, we investigate the influence of level of generosity and extortion on the evolutionary dynamics of generous and extortionate ZD, which was commonly ignored in previous studies. Theoretical results show players with limited generosity are at an advantageous place and extortioners extorting more severely hold their ground more readily. Our results may provide new insights into better understanding the evolutionary dynamics of ZD strategies in repeated multiplayer games.
The deer tick, $textit{Ixodes scapularis}$, is a vector for numerous human diseases, including Lyme disease, anaplasmosis, and babesiosis. Concern is rising in the US and abroad as the population and range of this species grow and new diseases emerge
. Herein I consider the potential for control of $textit{I. scapularis}$ using the Sterile Insect Technique (SIT), which acts by reducing net fertility through release of sterile males. I construct a population model with density-dependent and -independent growth, migration, and an Allee effect (decline of the population when it is small), and use this model to simulate sterile tick release in both single- and multi-patch frameworks. I test two key concerns with implementing $textit{I. scapularis}$ SIT: that the ticks lengthy life course could make control take too long and that low migration might mean sterile males need thorough manual dispersal to all parts of the control area. Results suggest that typical $textit{I. scapularis}$ SIT programs will take about eight years, a prediction near the normal range for the technique, but that thorough distribution of sterile ticks over the control area is indeed critical, increasing expense substantially by necessitating aerial release. With particularly high rearing costs also expected for $textit{I. scapularis}$, the latter finding suggests that cost-effectiveness improvements to aerial release may be a prerequisite to $textit{I. scapularis}$ SIT.
We revisit the spatial ${lambda}$-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the entire two-
dimensional plane, and on a finite rectangle. Utilizing a differential equation linking $T_0$ with the physical distance between the lineages, we arrive at simple and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model comes down from infinity, which has been partly answered before in [2].
We consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Fu
rther, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter. The most significant finding is the observation of a critical Allee parameter beyond which the probability of obtaining extreme events becomes non-zero for all three population densities. Though the emergence of extreme events in the predator population is not affected much by the Allee effect, the prey population shows a sharp increase in the probability of obtaining extreme events after a threshold value of the Allee parameter, and the vegetation population also yields extreme events for sufficiently strong Allee effect. Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This suggests that noise can mitigate extreme events, and has potentially important bearing on the observability of extreme events in naturally occurring systems.
Personal responsibility, one of the basic principles of modern law, requires one to be responsible for what he did. However, personal responsibility is far from the only norm ruling human interactions, especially in social and economic activities. In
many collective communities such as among enterprise colleagues and family members, ones personal interests are often bound to others -- once one member breaks the rule, a group of people have to bear the punishment or sanction. Such a mechanism is termed joint liability. Although many real-world cases have demonstrated that joint liability helps to maintain collective collaboration, a deep and systematic theoretical analysis on how and when joint liability promotes cooperation is lacking. Here we use evolutionary game theory to model an interacting system with joint liability, where ones losing credit could deteriorate the reputation of the whole group. We provide the analytical condition to predict when cooperation evolves in the presence of joint liability, which is verified by simulations. We also analytically prove that joint liability can greatly promote cooperation. Our work stresses that joint liability is of great significance in promoting the current economic propensity.
